I was considering using natural cubic splines for my prediction problem when I had a thought: In Ridge Regression, you set out to minimize the equation; \begin{equation} F(X)=\lambda\sum_i ( b^2)+ \sum_i (b^T x_i - y_i)^2. \end{equation}
Where the first term acts as a punishment for selecting beta too large.
I was thinking, could this be applied to a natural cubic spline setting in terms of number of knots? That way, you wouldn't have to manually select the number of knots and knot locations you could just train it to find it for you.
Thoughts?